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Fractional linear transformations. Definition. We let GL(2, C) be the set of invertible 2 2 matrices
 

Summary: Fractional linear transformations.
Definition. We let GL(2, C) be the set of invertible 2 2 matrices
a b
c d
with complex entries. Note that
(i) The identity matrix
I =
1 0
0 1
is in GL(2, C).
(ii) If A and B are in GL(2, C) then AB GL(2, C).
(iii) if A GL(2, C) then
A-1
=
1
ad - bc
d -b
-c a
is in GL(2, C).
That is, GL(2, C) is a group of matrices.

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics